1 Batch correction - GSM3872442 set

When we do single cell RNA-Seq experiments most of the time inevitably there will be technical batch effects. For example, logistically maybe we can’t put all of our samples in the same run and so have to split them up. Even within samples all sequenced together there can be batch effects from the previous steps. We need to check and correct for them.

1.1 Learning objectives

Understand different batch correction methods using one sample sequenced in two different runs. We will look at differences in :

  • Normalisation order

  • Correction with limma

  • Correction with mnnCorrect

  • Correction with fastMNN

  • Correction with Harmony

1.2 Data

GSM3872442 is a single PBMMC sample sequenced as a pool of two libraries: SRR9264351 and SRR9264352.

We will use this sample to illustrate batch correction methods.

Load object

sce <- readRDS("~/Downloads/caron_sce_nz_postQc.Rds")

Select the GSM3872442 cells:

sample1.nz.sce <- SingleCellExperiment(list(counts=counts(sce[, sce$Run %in% c("SRR9264351")])),
                                       colData=colData(sce[, sce$Run %in% c("SRR9264351")]))

sample2.nz.sce <- SingleCellExperiment(list(counts=counts(sce[, sce$Run %in% c("SRR9264352")])),
                                       colData=colData(sce[, sce$Run %in% c("SRR9264352")]))

saveRDS(sample1.nz.sce, "Robjects/BC_sample1.rds")
saveRDS(sample2.nz.sce, "Robjects/BC_sample2.rds")
sample1.sce <- readRDS("Robjects/BC_sample1.rds")
sample2.sce <- readRDS("Robjects/BC_sample2.rds")

1.3 Normalise each separately and re-pool

sample1.qclusters <- quickCluster(sample1.sce, method="igraph")
sample1.sce <- computeSumFactors(sample1.sce, min.mean=0.1, cluster=sample1.qclusters)
sample1.sce <- logNormCounts(sample1.sce)

sample2.qclusters <- quickCluster(sample2.sce, method="igraph")
sample2.sce <- computeSumFactors(sample2.sce, min.mean=0.1, cluster=sample2.qclusters)
sample2.sce <- logNormCounts(sample2.sce)

Re-pool:

# recombine the normalized samples together
all.samp.exprs <- do.call(cbind,
                          list("SRR9264351"=exprs(sample1.sce),
                               "SRR9264352"=exprs(sample2.sce)))
colnames(all.samp.exprs) <- c(as.character(colData(sample1.sce)$Barcode),
                              as.character(colData(sample2.sce)$Barcode))

For the PCA we want to quickly select the genes that are most informative. We will use the top 2000 genes with the highest variance.

gene.variances <- apply(all.samp.exprs, 1, var)
names(gene.variances) <- rownames(all.samp.exprs)
highly.variable.genes <- names(gene.variances[order(gene.variances, decreasing=TRUE)])[1:2000]

Perform PCA:

# we need to use a fast approximate algorithm for PCA on large data sets
# this algorithm has a stochastic component,
# so we need to fix the seed number to get the same result each time
set.seed(42)
separate.hvg.pca <- irlba::prcomp_irlba(t(all.samp.exprs[highly.variable.genes, ]), n=5) # we only need a few components
separate.hvg.pcs <- as.data.frame(separate.hvg.pca$x) # extract the principal components
separate.hvg.pcs$Cell <- colnames(all.samp.exprs) # set the sample column as the cell IDs

# combine the PCs with the sample information into a single data frame for plotting
samples.info <- data.frame("Cell"=colnames(all.samp.exprs),
                           "Run"=c(rep("SRR9264351", ncol(sample1.sce)), 
                                   rep("SRR9264352", ncol(sample2.sce))))

# merge the two data frames together
separate.pca.merge <- merge(separate.hvg.pcs, samples.info, by='Cell')
ggplot(separate.pca.merge, aes(x=PC1, y=PC2, fill=Run)) +
  geom_point(shape=21, size=3) +
  theme_minimal()

Plot PC1-PC2 plane, with cells colored by ‘Run’ (and sized according to library size):

sce.sep <- cbind(sample1.sce, sample2.sce)

sce.sep <- runPCA(sce.sep)

plotPCA(sce.sep, colour_by="Run", size_by = "sum")

sce.sep <- runTSNE(sce.sep, dimred="PCA")
plotTSNE(sce.sep, colour_by="Run", size_by = "sum")

sce.sep <- runUMAP(sce.sep, dimred="PCA")
plotUMAP(sce.sep, colour_by="Run", size_by = "sum")

1.4 Normalise batches together

sample3.sce <- SingleCellExperiment(list(counts=counts(sce[, sce$Run %in% c("SRR9264351", "SRR9264352")])),
                                       colData=colData(sce[, sce$Run %in% c("SRR9264351", "SRR9264352")]))

sample3.qclusters <- quickCluster(sample3.sce, method="igraph")
sample3.sce <- computeSumFactors(sample3.sce, min.mean=0.1, cluster=sample3.qclusters)
sample3.sce <- logNormCounts(sample3.sce)

pool.exprs <- exprs(sample3.sce)
colnames(pool.exprs) <- gsub(colData(sample3.sce)$Barcode, pattern="-", replacement=".")

Find the 2000 genes with the highest variance:

gene.variances <- apply(pool.exprs, 1, var)
names(gene.variances) <- rownames(pool.exprs)
highly.variable.genes <- names(gene.variances[order(gene.variances, decreasing=TRUE)])[1:2000]

Perform PCA:

# we need to use a fast approximate algorithm for PCA on large data sets
# this algorithm has a stochastic component, so we need to fix the seed number to get the same result each time
set.seed(42)
combined.hvg.pca <- irlba::prcomp_irlba(t(pool.exprs[highly.variable.genes, ]), n=5) # we only need a few components
combined.hvg.pcs <- as.data.frame(combined.hvg.pca$x) # extract the principal components
combined.hvg.pcs$Cell <- colnames(pool.exprs) # set the sample column as the cell IDs

# combine the PCs with the sample information into a single data frame for plotting
samples.info <- data.frame("Cell"=colnames(pool.exprs),
                           "Run"=colData(sample3.sce)$Run)

# merge the two data frames together
combined.pca.merge <- merge(combined.hvg.pcs, samples.info, by='Cell')

Plot PC1-PC2 plane, with cells colored by ‘Run’ (and sized according to library size):

sample3.sce <- runPCA(sample3.sce)
plotPCA(sample3.sce, colour_by="Run", size_by = "sum")

sample3.sce <- runTSNE(sample3.sce, dimred="PCA")
plotTSNE(sample3.sce, colour_by="Run", size_by = "sum")

sample3.sce <- runUMAP(sample3.sce, dimred="PCA")
plotUMAP(sample3.sce, colour_by="Run", size_by = "sum")

1.5 Batch correction

sample3.sce$Run <- factor(sample3.sce$Run)
sample3.sce$batch <- sample3.sce$Run

1.5.1 Gaussian (normal) linear models

Limma

suppressMessages(require(limma))
lm_design_batch <- model.matrix(~0 + batch, data = colData(sample3.sce))
fit_lm_batch <- lmFit(logcounts(sample3.sce), lm_design_batch)
resids_lm_batch <- residuals(fit_lm_batch, logcounts(sample3.sce))
assay(sample3.sce, "lm_batch") <- resids_lm_batch

reducedDim(sample3.sce, "PCA_lm_batch") <- reducedDim(
  runPCA(sample3.sce, exprs_values = "lm_batch"), "PCA")

plotReducedDim(sample3.sce, dimred = "PCA_lm_batch",
        colour_by = "batch", 
        size_by = "sum",
        shape_by = "Sample.Name"
        ) +
  ggtitle("LM - regress out batch")

1.6 SCTransform

First make a copy of the SCE object (we will need one later).

# have log lib size
sample3.sce$log10sum <- log10(sample3.sce$sum)
# keep copy of SCE to draw from after SCTransform,
# which discard some genes TODO check-again/mention slow 'return all' option
sample3.sceOrig <- sample3.sce

1.7 mnnCorrect

1.7.1 Check presence of batch effect

Batchelor commands to make the two batches and identify highly variable genes for faster dimensionality reduction.

library(batchelor)
# Mind assayNames()
sce1 <- sample3.sce[, sample3.sce$Run == "SRR9264351"]
sce2 <- sample3.sce[, sample3.sce$Run == "SRR9264352"]
library(scran)
dec1 <- modelGeneVar(sce1)
dec2 <- modelGeneVar(sce2)
combined.dec <- combineVar(dec1, dec2)
chosen.hvgs <- combined.dec$bio > 0
summary(chosen.hvgs)
##    Mode   FALSE    TRUE 
## logical    7655    8974

As a diagnostic, we check that there actually is a batch effect across these datasets by checking that they cluster separately. Here, we combine the two SingleCellExperiment objects without any correction using the NoCorrectParam() flag, and we informally verify that cells from different batches are separated using a t-SNE plot.

There is a moderate batch effect.

library(scater)
combined <- correctExperiments(A=sce1, B=sce2, PARAM=NoCorrectParam())
## Warning in .eliminate_overlaps(colnames(colData(merged)), combine.coldata, :
## ignoring 'colData' fields with same name as 'batchCorrect' output
combined <- runPCA(combined, subset_row=chosen.hvgs)
combined <- runTSNE(combined, dimred="PCA")
combined <- runUMAP(combined, dimred="PCA")
plotPCA(combined, colour_by="batch")

plotTSNE(combined, colour_by="batch")

plotUMAP(combined, colour_by="batch")

reducedDim(sample3.sce, "PCA_noCor") <- reducedDim(combined, "PCA")
reducedDim(sample3.sce, "TSNE_noCor") <- reducedDim(combined, "TSNE")
reducedDim(sample3.sce, "UMAP_noCor") <- reducedDim(combined, "UMAP")

1.7.2 Correct batch effect with mnnCorrect

This is the initial method. It uses gene expression values to identify cells with similar expression patterns in both batches.

Let us get the normalised counts:

batch1 <- logcounts(sce1)
batch2 <- logcounts(sce2)
# returns a matrix with rownames only for the gene subset,
# at the top of the matrix
# preventing copy of that corrected matrix as an assay in the SCE object

# mmnCorrect returns the corrected gene expression matrix directly

y <- batchelor::mnnCorrect(
          batch1, batch2,  
      correct.all = TRUE,
          k = 20,
          sigma = 0.1,
          cos.norm.in = TRUE,
          svd.dim = 2
        )

Copy the corrected values to the SCE object:

assay(sample3.sce, "mnn") <- assay(y, "corrected")

Show reduced dimension plots and check for improved mixing of cells from the two sets:

sample3.sce <- runPCA(sample3.sce, exprs_values = "mnn")
plotPCA(sample3.sce, colour_by="batch")

reducedDim(sample3.sce, "PCA_mnn") <- reducedDim(sample3.sce, "PCA")
sample3.sce <- runTSNE(sample3.sce, dimred="PCA_mnn")
plotTSNE(sample3.sce, colour_by="batch")

reducedDim(sample3.sce, "TSNE_mnn") <- reducedDim(sample3.sce, "TSNE")
sample3.sce <- runUMAP(sample3.sce, dimred="PCA_mnn")
plotUMAP(sample3.sce, colour_by="batch")

reducedDim(sample3.sce, "UMAP_mnn") <- reducedDim(sample3.sce, "UMAP")

1.8 fastMNN

This method is faster than mnnCorrect as it identifies nearest neighbours after dimensionality reduction.

fx <- batchelor::fastMNN(
                      sample3.sce,
                      batch = sample3.sce$Run
            )

Copy the corrected values to the SCE object:

# fastMNN may drop some genes
# so we may not be able to keep the outcome in 'assay'
assay(sample3.sce, "fastmnn") <- assay(fx, "reconstructed")

Show reduced dimension plots and check for improved mixing of cells from the two sets:

fastmnn_pca <- runPCA(assay(sample3.sce, "fastmnn"), rank=2) # slow
reducedDim(sample3.sce, "PCA_fastmnn") <- fastmnn_pca$rotation

plotReducedDim(
  sample3.sce,
  dimred = "PCA_fastmnn",
  colour_by = "batch",
  size_by = "sum",
  shape_by = "Sample.Name"
) + ggtitle("PCA plot: fastMNN") 

sample3.sce <- runTSNE(sample3.sce, dimred="PCA_fastmnn")
plotTSNE(sample3.sce, colour_by="batch")

reducedDim(sample3.sce, "TSNE_fastmnn") <- reducedDim(sample3.sce, "TSNE")
sample3.sce <- runUMAP(sample3.sce, dimred="PCA_fastmnn")
plotUMAP(sample3.sce, colour_by="batch")

reducedDim(sample3.sce, "UMAP_fastmnn") <- reducedDim(sample3.sce, "UMAP")

1.9 Harmony

Harmony [Korsunsky2018fast] is a newer batch correction method, which is designed to operate on PC space. The algorithm proceeds to iteratively cluster the cells, with the objective function formulated to promote cells from multiple datasets within each cluster. Once a clustering is obtained, the positions of the centroids of each dataset are obtained on a per-cluster basis and the coordinates are corrected. This procedure is iterated until convergence. Harmony comes with a theta parameter that controls the degree of batch correction (higher values lead to more dataset integration), and can account for multiple experimental and biological factors on input (see variant of the ‘Hemberg course’).

library(harmony)
## Loading required package: Rcpp
reducedDim(sample3.sce, "PCA_logcounts") <- reducedDim(
  runPCA(sample3.sce, exprs_values = "logcounts")
)

#Seeing how the end result of Harmony is an altered dimensional reduction space created on the basis of PCA, we plot the obtained manifold here and exclude it from the rest of the follow-ups in the section.

pca <- as.matrix(reducedDim(sample3.sce, "PCA_logcounts"))
harmony_emb <- HarmonyMatrix(pca,
                 sample3.sce$batch,
                 theta=2,
                 do_pca=FALSE)
## Harmony 1/10
## Harmony 2/10
## Harmony 3/10
## Harmony 4/10
## Harmony 5/10
## Harmony 6/10
## Harmony 7/10
## Harmony 8/10
## Harmony 9/10
## Harmony converged after 9 iterations
reducedDim(sample3.sce, "harmony") <- harmony_emb

plotReducedDim(
    sample3.sce,
    dimred = 'harmony',
    colour_by = "batch",
    size_by = "sum",
    shape_by = "Sample.Name"
)

1.10 Session information

sessionInfo()
## R version 4.1.0 (2021-05-18)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.7
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_GB.UTF-8/en_GB.UTF-8/en_GB.UTF-8/C/en_GB.UTF-8/en_GB.UTF-8
## 
## attached base packages:
## [1] parallel  stats4    stats     graphics  grDevices utils     datasets 
## [8] methods   base     
## 
## other attached packages:
##  [1] harmony_0.1.0               Rcpp_1.0.7                 
##  [3] batchelor_1.8.0             limma_3.48.1               
##  [5] Cairo_1.5-12.2              BiocSingular_1.8.1         
##  [7] dplyr_1.0.7                 scran_1.20.1               
##  [9] scater_1.20.1               ggplot2_3.3.5              
## [11] scuttle_1.2.0               SingleCellExperiment_1.14.1
## [13] SummarizedExperiment_1.22.0 Biobase_2.52.0             
## [15] GenomicRanges_1.44.0        GenomeInfoDb_1.28.1        
## [17] IRanges_2.26.0              S4Vectors_0.30.0           
## [19] BiocGenerics_0.38.0         MatrixGenerics_1.4.0       
## [21] matrixStats_0.59.0         
## 
## loaded via a namespace (and not attached):
##  [1] bitops_1.0-7              tools_4.1.0              
##  [3] bslib_0.2.5.1             ResidualMatrix_1.2.0     
##  [5] utf8_1.2.1                R6_2.5.0                 
##  [7] irlba_2.3.3               vipor_0.4.5              
##  [9] uwot_0.1.10               DBI_1.1.1                
## [11] colorspace_2.0-2          withr_2.4.2              
## [13] tidyselect_1.1.1          gridExtra_2.3            
## [15] compiler_4.1.0            BiocNeighbors_1.10.0     
## [17] DelayedArray_0.18.0       labeling_0.4.2           
## [19] sass_0.4.0                scales_1.1.1             
## [21] stringr_1.4.0             digest_0.6.27            
## [23] rmarkdown_2.9             XVector_0.32.0           
## [25] pkgconfig_2.0.3           htmltools_0.5.1.1        
## [27] sparseMatrixStats_1.4.0   highr_0.9                
## [29] rlang_0.4.11              FNN_1.1.3                
## [31] DelayedMatrixStats_1.14.0 jquerylib_0.1.4          
## [33] generics_0.1.0            farver_2.1.0             
## [35] jsonlite_1.7.2            BiocParallel_1.26.1      
## [37] RCurl_1.98-1.3            magrittr_2.0.1           
## [39] GenomeInfoDbData_1.2.6    Matrix_1.3-4             
## [41] ggbeeswarm_0.6.0          munsell_0.5.0            
## [43] fansi_0.5.0               viridis_0.6.1            
## [45] lifecycle_1.0.0           stringi_1.7.2            
## [47] yaml_2.2.1                edgeR_3.34.0             
## [49] zlibbioc_1.38.0           Rtsne_0.15               
## [51] grid_4.1.0                dqrng_0.3.0              
## [53] crayon_1.4.1              lattice_0.20-44          
## [55] cowplot_1.1.1             beachmat_2.8.0           
## [57] locfit_1.5-9.4            metapod_1.0.0            
## [59] knitr_1.33                pillar_1.6.1             
## [61] igraph_1.2.6              codetools_0.2-18         
## [63] ScaledMatrix_1.0.0        glue_1.4.2               
## [65] evaluate_0.14             vctrs_0.3.8              
## [67] tidyr_1.1.3               gtable_0.3.0             
## [69] purrr_0.3.4               assertthat_0.2.1         
## [71] xfun_0.24                 rsvd_1.0.5               
## [73] RSpectra_0.16-0           viridisLite_0.4.0        
## [75] tibble_3.1.2              beeswarm_0.4.0           
## [77] cluster_2.1.2             bluster_1.2.1            
## [79] statmod_1.4.36            ellipsis_0.3.2